PolynomialTraits_d::PseudoDivision Concept Reference

Definition

This AdaptableFunctor computes the pseudo division of two polynomials \( f\) and \( g\).

Given \( f\) and \( g \neq 0\) this functor computes quotient \( q\) and remainder \( r\) such that \( D \cdot f = g \cdot q + r\) and \( degree(r) < degree(g)\), where \( D = leading\_coefficient(g)^{max(0, degree(f)-degree(g)+1)}\)

This functor is useful if the regular division is not available, which is the case if PolynomialTraits_d::Coefficient_type is not a Field. Hence in general it is not possible to invert the leading coefficient of \( g\). Instead \( f\) is extended by \( D\) allowing integral divisions in the internal computation.

Refines

AdaptableFunctor

CopyConstructible

DefaultConstructible

See also

Polynomial_d

PolynomialTraits_d

PolynomialTraits_d::PseudoDivision

PolynomialTraits_d::PseudoDivisionRemainder

PolynomialTraits_d::PseudoDivisionQuotient

Types
typedef void	result_type

Operations
result_type	operator() (PolynomialTraits_d::Polynomial_d f, PolynomialTraits_d::Polynomial_d g, PolynomialTraits_d::Polynomial_d &q, PolynomialTraits_d::Polynomial_d &r, PolynomialTraits_d::Coefficient_type &D)
	Computes the pseudo division with respect to the outermost variable \( x_{d-1}\).